Answers
The numeric values for the population function are given as follows:
Initial population: 49 individuals.Population after eight years: 292 individuals.How to find the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, each instance of the input variable in the function or in the expression is replaced by the value at which we want to find the numeric value.
The function giving the population after t years is defined as follows:
[tex]P(t) = \frac{340}{1 + 6e^{-0.45t}}[/tex]
The initial population is the numeric value at t = 0, that is, the lone instance of t is replaced by zero, hence:
[tex]P(0) = \frac{340}{1 + 6e^{-0.45(0)}} = \frac{340}{7} = 49[/tex]
After eight years, the population is given by the numeric value at t = 8, hence:
[tex]P(8) = \frac{340}{1 + 6e^{-0.45(8)}} = 292[/tex]
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Related Questions
What is the slope of the line that passes through the points (-5,2) and (-1,-6)
Answers
Answer:
Slope = -2
Step-by-step explanation:
Slope of Line passes through two Points [tex](x_{1},y_{1} )[/tex] and [tex](x_{2},y_{2} )[/tex]
is given by [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
So by Substitution
[tex]m=\frac{-6- 2 }{-1 - (-5)}=\frac{-8}{4} =-2[/tex]
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Equation of the line for the given graph in slope-intercept form is given by y = 5x -1.
As given in the question,
From the given graph,
Consider pair of two coordinates we have,
(x₁ , y₁) = (1, 4)
(x₂ , y₂) = (0,-1)
Equation of the line for the given graph in slope-intercept form is given by:
(y -y₁) / (x -x₁)= (y₂ -y₁) / (x₂ -x₁)
⇒ ( y - 4)/ (x -1) = (-1-4)/(0-1)
⇒(y-4)/(x-1) = 5
⇒y-4 = 5(x-1)
⇒y = 5x -5 +4
⇒ y= 5x -1
Therefore, equation of the line for the given graph in slope-intercept form is given by y = 5x -1.
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six thousand seven hundred and fifty (6750) people who were free of disease x were enrolled in a cohort study in 1985 and followed with annual exams and interviews through 1995. exposure to factor a was determined at study enrollment and the participants were followed until 1995 to observe new cases of disease x. data from the study at the end of follow-up are shown in the table (below). what is the incidence rate of disease x among persons exposed to factor a?
Answers
Option A is the correct choice (0.04)
The incidence rate of disease x among persons exposed to factor a is 0.04
The frequency of a particular incident over a predetermined time period is measured by the incidence rate or incidence. In the corporate world, sampling, surveys, and product testing can all be used to calculate an incidence rate.
Because 120 divided by the total number of exposed people yields the occurrence rate for disease X among those who have been exposed.
The incidence rate would be 4 per 100 people if multiplied by 100, however, this statistic is not specifically specified.
Therefore, those who were exposed to factor a had an incidence risk of disease x of 0.04
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COMPLETE QUESTION:
6,750 people who were free of disease X were enrolled in a cohort study in 1985 and followed by annual exams and interviews through 1995. Exposure to factor A was determined at study enrollment and the participants were followed until 1995 to observe new cases of disease X. Data from the study at the end of the follow-up are shown in the following table. What is the incidence rate of disease X among persons exposed to factor A? Exposure to Factor A People with Disease X People without Disease X Not Exposed 30 3,720 Exposed 120 2,880
Select one:
a. 0.04
b. 0.19
c. 0.25
d. 4.00
e. 5.17
The weight of four different boxes is shown in pounds. Which list shows the weights in order from least to greatest?
16.4, 16 1/2, 16.625 , 16 3/5
Answers
Answer: 16.4, 16 1/2, 16 3/5 16.625,
Step-by-step explanation: 16.4, 16 1/2, 16 3/5 16.625,
16 1/2 = 16.5, 16 3/5 = 16.6
An astronaut has an annual income of $161,141.00.
The income tax an astronaut must pay is 8%.
What is the amount of income tax in dollars and cents that the
astronaut must pay?
Answers
Jeanne has 3 7/8 yards of fabric. The table shows the amount of fabric she needs for different items. How many pairs of shorts can she make?
Answers
Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric.
What do you mean by ratio?
The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
The total amount of fabric = 3 7/8 yards = 31/8 yards.
Amount of fabric needed to make 1 pair of shorts = 1 1/4 = 5/4 yards.
The number of shorts that can be made = 31/8 ÷ 5/4
⇒ 3.1 so it will be 3 because no relevance of decimal shorts.
Hence "Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric".
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Juan has a piano recital next month. Last week he practiced for 4 hours in the morning and 9 hours in the afternoon. A full practice session is 2 hours long. How many full practice sessions does Juan complete?
Answers
6 practice sessions
Explanation:
(4 + 9)/2 = 6.5
We need to make it the number of full practice sessions, which is 6.
Christian buys 18 bottles of grapefruit juice at the corner store for a total cost of $15.66. If each bottle costs the same amount, how much is 3 bottles of juice?
Answers
Answer:$2.61
Step-by-step explanation:
18=$15.66
÷6 ÷6
3=$2.61
The cost of 3 bottles of juice based on the given ratio will be $2.61.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
18 bottles cost = $15.66
1 bottle cost = $15.66/18 = $0.87/ bottle
For 3 bottles = 3 × $0.87 = $2.61
Hence "The cost of 3 bottles of juice based on the given ratio will be $2.61".
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Brian loves to bake blueberry muffins for his friends and family.
there is a proportional relationship between the volume of flour brian uses (in cups), x, and
the number of muffins he bakes, y.
10
9
8
7
9
s
s
3
2
2
s
9
00
9
10
Answers
For a proportional relationship between the volume of flour used (in cups), x, and the number of baked muffins, y, the constant of proportionality is 4.
Constant of proportionality, also known as constant ratio or constant rate, refers to is the ratio that relates two given values in a data set that is represented as a proportional relationship. When two parameters are proportional, either directly or indirectly, the relationship is expressed as a = kb or a = k/b, where k indicates the relationship between the two variables and is known as the proportionality constant. In the given data, the proportionality constant is:
k =b/a = 8/2 =12/3 = 16/4 = 20/4 = 4
Hence, the proportionality constant for the given data is 4.
Notes: The question is incomplete. The complete question is: Brian loves to bake blueberry muffins for his friends and family. There is a proportional relationship between the volume of flour brian uses (in cups), x, and the number of muffins he bakes, y. What is the constant of proportionality. (Refer to the table).
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Please graph this equation y=4|x-1|+3
Answers
The graph of equation y=4|x-1|+3 is as shown below.
In this question, we need to graph the equation y=4|x-1|+3
We know that the parent function of given equation is z = |x|
A parent function is translated right by 1 unit then it is dilated vertically by 4 units and the resulting image is translated up by 3 units.
The graph of equation y=4|x-1|+3 is as shown below.
The vertex of equation y=4|x-1|+3 is at (1, 3)
Therefore, the graph of equation y=4|x-1|+3 is as shown below.
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G(F(x)) = (x - 5)3 + x - 5
A.
F(x) = x - 5 and G(x) = (x - 5)3
B.
F(x) = x - 5 and G(x) = x3 + x
C.
F(x) = (x - 5)3 and G(x) = x - 5
D.
F(x) = x3 + x - 5 and G(x) = x - 5
Answers
Option B is correct.
Given that Function G(F(x)) = (x - 5)3 + x - 5 ;
Lets take a function G(x) = x3 + x as (i) and check that it will produce the above equation or not.
Now suppose that the value of the function F(x) = x-5 as (ii) , using this value we will check that whether it support the value for g(x) or not.
Put the value of function f(x) in the equation number i , it will be like this :
G(f(x)) = f(x)3 + f(x)
we know that the value of f(x) from (ii)
Therefore, G(f(x)) will be :
G(f(x)) = (x - 5)3 + x - 5, this will satisfy the above equation which means our supposition was correct. Hence the correct ans is B
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the ph measurements of water specimens from various locations along a given river basin are normally distributed with mean 8 and standard deviation 0.3. what is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2? 0.7475 0.2525 0.7525 0.2475
Answers
0.7475 is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2
P( A ≥ 8.2) = P( (Z ≥ 8.2 − 8)/0.3)
= P(Z ≥0.66)
= 0.7475
normsdist(0.666666) =0.7475
The standard normal cumulative distribution function is returned. The mean of the distribution is 0 (zero), while the standard deviation is one. Instead of a table of standard normal curve areas, use this function.The concentration of hydronium (H3O+) ions in an aqueous solution is measured by pH. It is measured from 0 to 14 on a negative logarithmic scale.
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what is the mean of 10,4,2,4
Answers
Answer:
5
Step-by-step explanation:
10+4+2+4=20
20/4=5
The mean is five.
Answer:
Mean = 5
Step-by-step explanation:
Mean = ( Sum of Data Points ) / ( Number of Data Points )
Sum of Data Points = 10 + 4 + 2 + 4 = 20
Number of Data Points = 4
Mean = 20 / 4 = 5
Glad to Help
III. Write each quadratic equation in standard form
1. 3x-2x² = 7
2.5-2x² = 6x
3.(x+3)(x+4)=0
4.(2x + 7)(x-1)=0
5,2x(x-3) = 15
ax²+bx+c=0
Answers
Answers are attached
help meeeeeeeeeeeeeee pleaseee
Answers
Answer:
You have to place the numbers given or your left in the formula given. So for example: y= 2*(-2)^2
that's: y=2*4, so: y=8
1) y=8
2) y= 2*(-1)^2. y=2
3) y= 2*(0)^2. y=0
4) y= 2*(1)^2. y=2
5) y= 2*(2)^2. y=8
Kelly went to a store to purchase a coffee pot. She will use a coupon for 20% off. She can calculate the cost before sales tax using the following expression, where c represents the original cost of the coffee pot.
c−0.2c
Which other expression could Kelly use to calculate her cost before sales tax?
Answers
Answer:
0.2c-c
Step-by-step explanation:
what are the coefficients in 4x + 8y - 5
Answers
Answer:
Step-by-step explanation:
A coefficient is a number before the variable that shows how many groups of the variable there are. For example, 2b would be two groups of B.
The coefficients in this expression would be 4 (as in 4x) and 8 (as in 8y).
Which ordered pair gives a solution of the system of equations represented in
the graph below?
A. (-1.5, 2.5)
B. (-2.5, 1.5)
C. (2.5, -1.5)
D. (2.5,1.5)
Answers
Answer: The correct answer is D. (2.5,1.5)
Step-by-step explanation:
As noted in the graph, the lines intersect at the location where x=2.5 and y=1.5 in Quadrant I (both positive).
If J is the centroid of CDE, DE = 52, FC = 15,
and HE = 14, find each missing measure.
Answers
The measure of missing line segments will be:
DG = 26; GE = 26; DF = 15; CH = 14; CE = 28
What is centroid?The centroid of a triangle is the place where the three medians of the triangle connect. It is sometimes defined as the point at where the three medians cross. A median line connects the middle of a side to the opposing vertex of a triangle. The centroid of a triangle is the point at where the triangle's three medians coincide (each median connecting a vertex with the midpoint of the opposite side).
Here,
IF If J is the centroid of CDE, this means that J divides CG, FE, DC, CE and DH into two equal parts.
The following expressions are therefore true
DG + GE = DE and DG = GE
Substituting
DG + DG = DE
2DG = DE
Given DE = 52
2DG = 52
DG = 52/2
DG = 26
Since DG = GE, hence GE = 26
Also DF + FC = DC and DF = FC
Since FC = 15, hence DF = 15
Also CH + HE = CE and CH = HE
Since HE = 14, hence CH = 14
CE = 14+14
CE = 28
The missing line segment count will be: DG = 26; GE = 26; DF = 15; CH = 14; CE = 28.
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The approximate average distances from the sun to Mars and Mercury are listed below:
Mars: 2.28\times 10^{8}2.28×10
8
kilometers
Mercury: 5.79\times 10^{7}5.79×10
7
kilometers
How much farther from the sun is Mars? Express your answer using scientific notation?
Answers
The distance from the Sun to Mars is 3. 9 times farther
What is ratio?Ratio can be described as a mathematical comparison between two or more numbers or elements in relation to each other on the basis of their sizes or magnitudes.
It is however known to show how many times one number or elements contains another.
Based on the information given, we have;
Distance from the Sun to Mars = 2.28×10^8Distance from the Sun to Mercury = 5.79×10^7To determine the ratio of their distances from the Sun, we have;
Distance from the Sun to Mars /Distance from the Sun to Mercury
Substitute the values
2.28×10^8/5.79×10^7
Divide through
3. 9 times
Hence, the distance is 3. 9 times farther.
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wade is skiing on a circular ski trail that has a radius of 0.8 km. wade starts at the 3-o'clock position and travels 2.3 km in the counter-clockwise direction. how many radians does wade sweep out? 2.875 correct radians when wade stops skiing, how many km is wade to the right of the center of the ski trail? .7717 incorrect km when wade stops skiing, how many km is wade above of the center of the ski trail?
Answers
The solutions are,
The radians wade sweep out is 2.875 radians.
When wade stops skiing, he is 0.799km to the right of the center of the ski trail.
When wade stops skiing, he is 0.003km above the center of the ski trail.
Given that;
Wade is traveling along a 0.8 km-radius circular ski trail. Wade moves 2.3 kilometers counterclockwise starting at the three o'clock position.
Radius (r) = 0.8km
Distance (s) = 2.3km
Here, we need to find three cases, they are;
Case(I): how many radians does wade sweep out;
The relation between radians and radius is given by,
s = rθ
2.3 = 0.8*θ
θ = 2.3/0.8
θ = 2.875
The radians wade sweep out is 2.875 radians.
Case (II): when wade stops skiing, how many km is wade to the right of the center of the ski trail;
Let, Ф = π - 2.875
Ф = 0.266 radians
Then, x = r*cosФ
x = 0.8*cos(0.266)
x = 0.799
When wade stops skiing, he is 0.799km to the right of the center of the ski trail.
Case (III): when wade stops skiing, how many km is wade above the center of the ski trail;
Let, y = r*sinФ
y = 0.8*sin(0.266)
y = 0.003
When wade stops skiing, he is 0.003km above the center of the ski trail.
Therefore, the required solutions are;
The radians wade sweep out is 2.875 radians.
When wade stops skiing, he is 0.799km to the right of the center of the ski trail.
When wade stops skiing, he is 0.003km above the center of the ski trail.
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yesterday, Austin burned 199 calories while exercising. Today, he burned 1008.8 calories. How many more calories did Austin burn today than yesterday?
Answers
Answer: Austin burn 809.8 more calories today than yesterday.
What are the coordinates of the vertices after a rotation 90 counterclockwise around the origin.
Answers
Answer:When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
Step-by-step explanation: trust me
14x²y – 21xy² + 28x²y²
Answers
Answer:
7xy(2x-3y+4xy)
Step-by-step explanation:
14÷7=2
21÷7=3
28÷7=4
they all have 7, x and y so that would be on the outside
The length of the base of an isosceles triangle is x. The length of a leg is 4x-3. The perimeter of the triangle is 129 Find x.
Answers
The value of x in the given isosceles triangle is x = 15
Perimeter of an isosceles triangle: Calculating the value of xFrom the question, we are to determine the value of x.
From the given information,
The length of the base of the isosceles triangle is x
Also,
The length of a leg is 4x - 3
Since, the length of the legs of an isosceles triangle are equal,
Then,
The length of the other leg is 4x - 3
Also, form the given information,
The perimeter of the triangle is 129
Thus,
x + 4x - 3 + 4x - 3 = 129
Now, solve for x
x + 4x - 3 + 4x - 3 = 129
Collect like terms
x + 4x + 4x = 129 + 3 + 3
9x = 135
Divide both sides by 9
9x/9 = 135/9
x = 15
Hence, the value of x is 15
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At the local petting zoo, 65% of the goats are female. A researcher selects a sample of five and the goats and notes that three are female. What are p nd p^(p-hat) for female goats?
Answers
The values of p and ρˆ (p-hat) in the sample are
p = 0.65 and ρˆ (p-hat) = 0.4
How to determine the values of p and ρˆ (p-hat)?From the question, we have the following parameters that can be used in our computation:
Proportion of female goats = 65%
Sample = 5
Female = 3
The proportion of female represents the variable p
So, we have
p = Proportion of female = 65%
This gives
p = 65%
Express as decimal
p = 0.65
The variable ρˆ (p-hat) is then calculated as
ρˆ = x/n
In this case,
x = Female = 2
n = Male + Female = 2 + 3 = 5
So, we have
ρˆ = 2/5
Evaluate
ρˆ = 0.4
Hence, the values are 0.48 and 0.44, respectively
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How can the dimensions of algebra tile rectangles and area models be used to represent expressions and multiplication?
Answers
The dimensions of algebra tile rectangles and area models can be used to represent expressions and multiplication by measuring the length and breadth of the tiles and multiplying them.
What is a Rectangle?This is referred to as a quadrilateral which has four right angles and the area is calculated by multiplying the length with the breadth.
In as situation where the algebra tile rectangles is used , it is best to first measure the length and the breadth after which they are then multiplied to give the appropriate answer. For example if the length is 8cm and the breadth is 5cm then the area will be 8cm × 5cm = 40cm²
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Write your answers hhere
Answers
Answer:
Step-by-step explanation:
The answer is 6.
I got this by subtracting 23 by 12 (the number of numbers shown). Then I got 11. So I followed the pattern until I got six.
23-12=11
2,4,6,8,2,4,6,8,2,4,6,8,......2,4,6,8,2,4,6,8,2,4,6
The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second number? Justify your reasoning
.
Answers
Answer:
40
Step-by-step explanation:
Looking at the other examples, its shows the the second number is always 4 times bigger/ahead then/of the first number.
Question 5 (5 points)
Find the equation of the line passing through the point (-1, 5) and perpendicular to
the line y=-3x+4.
A) 3y=-x+16
B) 3y=x+16
OC) y=-3x+8
D) y=-3x+2
OLD
Answers
Answer:
Option B is perpendicular to y=-3x+4 and goes through point (-1,5)
Step-by-step explanation:
We will look for an equation of the form y=mx+b, where m is the slope and b the y-intercept. The reference line, y=-3x+4, has a slope of -3. A line perpendicular to this line will have a slope that is the "negative inverse" of the refence lines slope. In this case, it's slope would be +(1/3).
We could graph each of the equation options and look for one that is perpendicular, but it might be faster to simply rearrnaged the options into standard format of y=mx+b. which we'll do here:
Option Rearranged Equation Slope
A) 3y=-x+16
y = -(1/3)x+(16/3) -(1/3)
B) 3y=x+16
y = (1/3)x + (16/3) (1/3)
C) y=-3x+8 -3
D) y=-3x+2 -3
There is only one option that has the required slope to be parallel to the reference equation (y=-3x+4), option B: y = (1/3)x + (16/3)
Does it go through point (-1,5)?
y = (1/3)x + (16/3)
Enter x = -1 and find 5:
y = (1/3)(-1) + (16/3)
y = (16/3)-(1/3)
y = (15/3) or 5
Yes, it goes through point (-1,5)
Option B is perpendicular to y=-3x+4 and goes through point (-1,5).